Authors list

  1. Danial Habibi
  2. Mahdi Akbarzadeh
  3. Farshad Teymoori
  4. Sahand Tehrani Fateh
  5. Sajedeh Masjoudi
  6. Amir Hossein Saeidian
  7. Farhad Hosseinpanah
  8. Noushin Mosavi
  9. Hakon Hakonarson
  10. Fereidoun Azizi
  11. Alireza Soleymani T
  12. Mehdi Hedayati
  13. Maryam Sadat Daneshpour
  14. Marjan Mansourian

[ANG]

Introduction

  • Title: Investigating the causality between Monounsaturated Fatty Acids on Cardiovascular Disease

Data Preparation

1- Number of total SNPs in exposure: 12,321,875 SNPs

2- Number of Selected SNPs exposure: 44 SNPs

3- Number of total SNPs in outcome: 9,851,867 SNPs

4- Number of common variants between exposure and outcome: 37 SNPs

5- Number of SNPs after harmonization (action=2) = 36 SNPs

6- Number of SNPs after removing HLA region with exploring in HLA Genes, Nomenclature = 36 SNPs

7- Number of SNPs after removing those that have MAF < 0.01 = 36 SNPs

8- Checking pleiotropy by PhenoScanner:

How many SNPs have been eliminated after checking the PhenoScanner website: 4 SNPs (rs115849089, rs1260326, rs429358, and rs56289821)

Checking weakness of the instruments

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   21.29   22.20   24.82   29.35   27.70   81.06

How many SNPs have been eliminated with checking the weakness: 0 SNP

RUN an initial MR:

Initial MR analysis
id.exposure id.outcome outcome exposure method nsnp b se pval
w10boa 0DIRXV outcome exposure MR Egger 32 0.0092767 0.0035303 0.0134136
w10boa 0DIRXV outcome exposure Weighted median 32 0.0045031 0.0014980 0.0026468
w10boa 0DIRXV outcome exposure Inverse variance weighted 32 0.0043228 0.0012409 0.0004945
w10boa 0DIRXV outcome exposure Simple mode 32 0.0085288 0.0032231 0.0126736
w10boa 0DIRXV outcome exposure Weighted mode 32 0.0076863 0.0030941 0.0185940

Heterogeneity testing
id.exposure id.outcome outcome exposure method Q Q_df Q_pval
w10boa 0DIRXV outcome exposure MR Egger 47.16615 30 0.0239700
w10boa 0DIRXV outcome exposure Inverse variance weighted 50.67952 31 0.0143121
pleiotropy testing
id.exposure id.outcome outcome exposure egger_intercept se pval
w10boa 0DIRXV outcome exposure -0.0004509 0.0003016 0.1453901

Testing Outlier with PRESSO test

## $`Main MR results`
##        Exposure       MR Analysis Causal Estimate         Sd   T-stat
## 1 beta.exposure               Raw     0.004322811 0.00124086 3.483722
## 2 beta.exposure Outlier-corrected              NA         NA       NA
##       P-value
## 1 0.001496903
## 2          NA
## 
## $`MR-PRESSO results`
## $`MR-PRESSO results`$`Global Test`
## $`MR-PRESSO results`$`Global Test`$RSSobs
## [1] 54.70446
## 
## $`MR-PRESSO results`$`Global Test`$Pvalue
## [1] 0.015
## 
## 
## $`MR-PRESSO results`$`Outlier Test`
##          RSSobs Pvalue
## 1  8.029625e-07  0.672
## 2  1.684675e-07      1
## 3  1.924740e-07      1
## 4  1.843632e-07      1
## 5  1.225485e-07      1
## 6  2.368531e-07      1
## 7  2.508848e-07      1
## 8  1.021119e-07      1
## 9  2.426335e-07      1
## 10 1.662435e-07      1
## 11 1.308346e-06      1
## 12 5.904347e-08      1
## 13 9.220546e-07  0.576
## 14 1.009905e-07      1
## 15 6.716404e-07      1
## 16 1.390861e-07      1
## 17 7.805953e-09      1
## 18 8.297846e-07      1
## 19 6.893822e-09      1
## 20 2.248506e-07      1
## 21 1.210955e-07      1
## 22 4.142234e-11      1
## 23 2.921072e-08      1
## 24 1.885866e-08      1
## 25 7.331039e-07      1
## 26 7.803325e-06  0.096
## 27 2.196524e-07      1
## 28 4.488497e-09      1
## 29 3.509989e-08      1
## 30 9.982133e-07      1
## 31 1.658861e-07      1
## 32 2.712064e-06   0.16
## 
## $`MR-PRESSO results`$`Distortion Test`
## $`MR-PRESSO results`$`Distortion Test`$`Outliers Indices`
## [1] "No significant outliers"
## 
## $`MR-PRESSO results`$`Distortion Test`$`Distortion Coefficient`
## [1] NA
## 
## $`MR-PRESSO results`$`Distortion Test`$Pvalue
## [1] NA
## [1] "One SNP (rs591592) were detected by MRPRESSO and excluded for further analyses"
MR analysis after excluding SNPs detected by MRPRESSO
id.exposure id.outcome outcome exposure method nsnp b se pval
w10boa 0DIRXV outcome exposure MR Egger 31 0.0090637 0.0036205 0.0181807
w10boa 0DIRXV outcome exposure Weighted median 31 0.0047626 0.0015305 0.0018600
w10boa 0DIRXV outcome exposure Inverse variance weighted 31 0.0044562 0.0012662 0.0004325
w10boa 0DIRXV outcome exposure Simple mode 31 0.0085243 0.0032072 0.0124861
w10boa 0DIRXV outcome exposure Weighted mode 31 0.0076822 0.0030292 0.0166527

Heterogeneity testing
id.exposure id.outcome outcome exposure method Q Q_df Q_pval
w10boa 0DIRXV outcome exposure MR Egger 46.90949 29 0.0190151
w10boa 0DIRXV outcome exposure Inverse variance weighted 49.88295 30 0.0127539
pleiotropy testing
id.exposure id.outcome outcome exposure egger_intercept se pval
w10boa 0DIRXV outcome exposure -0.0004244 0.000313 0.1856232

Radial test

## 
## Radial IVW
## 
##                     Estimate    Std.Error  t value     Pr(>|t|)
## Effect (Mod.2nd) 0.004329998 0.0012410857 3.488879 4.850506e-04
## Iterative        0.004329998 0.0012410857 3.488879 4.850506e-04
## Exact (FE)       0.004577654 0.0009823369 4.659964 3.162650e-06
## Exact (RE)       0.004498928 0.0013155902 3.419703 1.775749e-03
## 
## 
## Residual standard error: 1.265 on 31 degrees of freedom
## 
## F-statistic: 12.17 on 1 and 31 DF, p-value: 0.00148
## Q-Statistic for heterogeneity: 49.61039 on 31 DF , p-value: 0.01832529
## 
##  No significant outliers 
## Number of iterations = 2
## [1] "No significant outliers"
## [1] "One SNP (rs964184) were detected by Radial and excluded for further analyses"
MR analysis after excluding SNPs detected by MRPRESSO
id.exposure id.outcome outcome exposure method nsnp b se pval
w10boa 0DIRXV outcome exposure MR Egger 31 0.0064702 0.0035991 0.0826389
w10boa 0DIRXV outcome exposure Weighted median 31 0.0036906 0.0015056 0.0142386
w10boa 0DIRXV outcome exposure Inverse variance weighted 31 0.0035168 0.0011925 0.0031864
w10boa 0DIRXV outcome exposure Simple mode 31 0.0083347 0.0031966 0.0140789
w10boa 0DIRXV outcome exposure Weighted mode 31 0.0074323 0.0030396 0.0205665

Heterogeneity testing
id.exposure id.outcome outcome exposure method Q Q_df Q_pval
w10boa 0DIRXV outcome exposure MR Egger 40.90141 29 0.0702423
w10boa 0DIRXV outcome exposure Inverse variance weighted 41.96936 30 0.0720070
pleiotropy testing
id.exposure id.outcome outcome exposure egger_intercept se pval
w10boa 0DIRXV outcome exposure -0.0002607 0.0002996 0.3913518

Cook’s distance

In statistics, Cook’s distance or Cook’s D is a commonly used estimate of the influence of a data point when performing a least-squares regression analysis.[1] In a practical ordinary least squares analysis, Cook’s distance can be used in several ways:

1- To indicate influential data points that are particularly worth checking for validity.

2- To indicate regions of the design space where it would be good to be able to obtain more data points.

It is named after the American statistician R. Dennis Cook, who introduced the concept in 1977.

Refernce

Run After deleting new outlier: Final Results:

MR analysis after deleting outliers
id.exposure id.outcome outcome exposure method nsnp b se pval
w10boa 0DIRXV outcome exposure MR Egger 25 0.0080165 0.0034233 0.0282202
w10boa 0DIRXV outcome exposure Weighted median 25 0.0063587 0.0016061 0.0000752
w10boa 0DIRXV outcome exposure Inverse variance weighted 25 0.0050631 0.0011313 0.0000076
w10boa 0DIRXV outcome exposure Simple mode 25 0.0087734 0.0029586 0.0067373
w10boa 0DIRXV outcome exposure Weighted mode 25 0.0082151 0.0027323 0.0061073

Heterogeneity testing
id.exposure id.outcome outcome exposure method Q Q_df Q_pval
w10boa 0DIRXV outcome exposure MR Egger 17.81368 23 0.7675161
w10boa 0DIRXV outcome exposure Inverse variance weighted 18.64924 24 0.7704279
pleiotropy testing
id.exposure id.outcome outcome exposure egger_intercept se pval
w10boa 0DIRXV outcome exposure -0.0002564 0.0002806 0.3701534

Sensitivity analyses with MendelianRandomization Package

## 
## Inverse-variance weighted method
## (variants uncorrelated, random-effect model)
## 
## Number of Variants : 28 
## 
## ------------------------------------------------------------------
##  Method Estimate Std Error 95% CI       p-value
##     IVW    0.005     0.001 0.003, 0.007   0.000
## ------------------------------------------------------------------
## Residual standard error =  0.911 
## Residual standard error is set to 1 in calculation of confidence interval when its estimate is less than 1.
## Heterogeneity test statistic (Cochran's Q) = 22.3877 on 27 degrees of freedom, (p-value = 0.7174). I^2 = 0.0%.
##                     Method Estimate Std Error 95% CI        P-value
##              Simple median    0.006     0.002   0.003 0.009   0.000
##            Weighted median    0.006     0.002   0.003 0.009   0.000
##  Penalized weighted median    0.006     0.002   0.004 0.009   0.000
##                                                                    
##                        IVW    0.005     0.001   0.003 0.007   0.000
##              Penalized IVW    0.005     0.001   0.003 0.007   0.000
##                 Robust IVW    0.005     0.001   0.003 0.007   0.000
##       Penalized robust IVW    0.005     0.001   0.003 0.007   0.000
##                                                                    
##                   MR-Egger    0.008     0.003   0.002 0.014   0.009
##                (intercept)    0.000     0.000  -0.001 0.000   0.279
##         Penalized MR-Egger    0.008     0.003   0.002 0.014   0.009
##                (intercept)    0.000     0.000  -0.001 0.000   0.279
##            Robust MR-Egger    0.008     0.003   0.001 0.015   0.019
##                (intercept)    0.000     0.000  -0.001 0.000   0.355
##  Penalized robust MR-Egger    0.008     0.003   0.001 0.015   0.019
##                (intercept)    0.000     0.000  -0.001 0.000   0.355

id.exposure id.outcome exposure outcome snp_r2.exposure snp_r2.outcome correct_causal_direction steiger_pval
w10boa 0DIRXV exposure outcome 0.001838 8.94e-05 TRUE 0
## $r2_exp
## [1] 0
## 
## $r2_out
## [1] 0.25
## 
## $r2_exp_adj
## [1] 0
## 
## $r2_out_adj
## [1] 0.25
## 
## $correct_causal_direction
## [1] FALSE
## 
## $steiger_test
## [1] 0
## 
## $correct_causal_direction_adj
## [1] FALSE
## 
## $steiger_test_adj
## [1] 0
## 
## $vz
## [1] NaN
## 
## $vz0
## [1] 0
## 
## $vz1
## [1] NaN
## 
## $sensitivity_ratio
## [1] NaN
## 
## $sensitivity_plot

Working with MRraps

## $beta.hat
## [1] 0.005121877
## 
## $beta.se
## [1] 0.00112464
## 
## $beta.p.value
## [1] 5.257628e-06
## 
## $naive.se
## [1] 0.001104662
## 
## $chi.sq.test
## [1] 21.74294
##   over.dispersion loss.function    beta.hat     beta.se
## 1           FALSE            l2 0.005121877 0.001124640
## 2           FALSE         huber 0.005279650 0.001156012
## 3           FALSE         tukey 0.005289270 0.001156148
## 4            TRUE            l2 0.005136566 0.001147648
## 5            TRUE         huber 0.005278331 0.001157411
## 6            TRUE         tukey 0.005289602 0.001157629
## 
## Constrained maximum likelihood method (MRcML) 
## Number of Variants:  28 
## Results for:  cML-MA-BIC 
## ------------------------------------------------------------------
##      Method Estimate    SE Pvalue        95% CI
##  cML-MA-BIC    0.005 0.001  0.000 [0.003,0.007]
## ------------------------------------------------------------------
## 
## Debiased inverse-variance weighted method
## (Over.dispersion:TRUE)
## 
## Number of Variants : 28 
## ------------------------------------------------------------------
##  Method Estimate Std Error 95% CI       p-value Condition
##    dIVW    0.005     0.001 0.003, 0.007   0.000   142.585
## ------------------------------------------------------------------
## 
## Mode-based method of Hartwig et al
## (weighted, delta standard errors [not assuming NOME], bandwidth factor = 1)
## 
## Number of Variants : 28 
## ------------------------------------------------------------------
##  Method Estimate Std Error 95% CI       p-value
##     MBE    0.008     0.003 0.003, 0.013   0.002
## ------------------------------------------------------------------

[ASCVD]

Introduction

  • Title: Investigating the causality between Monounsaturated Fatty Acids on Cardiovascular Disease

Data Preparation

1- Number of total SNPs in exposure: 12,321,875 SNPs

2- Number of Selected SNPs exposure: 44 SNPs

3- Number of total SNPs in outcome: 9,851,867 SNPs

4- Number of common variants between exposure and outcome: 36 SNPs

5- Number of SNPs after harmonization (action=2) = 35 SNPs

6- Number of SNPs after removing HLA region with exploring in HLA Genes, Nomenclature = 35 SNPs

7- Number of SNPs after removing those that have MAF < 0.01 = 35 SNPs

8- Checking pleiotropy by PhenoScanner:

How many SNPs have been eliminated after checking the PhenoScanner website: 0 SNPs

Checking weakness of the instruments

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   21.34   22.36   24.96   31.10   30.73   86.31

How many SNPs have been eliminated with checking the weakness: 0 SNP

RUN an initial MR:

Initial MR analysis
id.exposure id.outcome outcome exposure method nsnp b se pval
Ae0Nt5 TcYOpY outcome exposure MR Egger 35 0.0109733 0.0049384 0.0332498
Ae0Nt5 TcYOpY outcome exposure Weighted median 35 0.0044997 0.0012533 0.0003304
Ae0Nt5 TcYOpY outcome exposure Inverse variance weighted 35 0.0057876 0.0016046 0.0003098
Ae0Nt5 TcYOpY outcome exposure Simple mode 35 0.0041996 0.0026274 0.1192024
Ae0Nt5 TcYOpY outcome exposure Weighted mode 35 0.0065586 0.0020791 0.0033544

Heterogeneity testing
id.exposure id.outcome outcome exposure method Q Q_df Q_pval
Ae0Nt5 TcYOpY outcome exposure MR Egger 126.6698 33 0
Ae0Nt5 TcYOpY outcome exposure Inverse variance weighted 131.3981 34 0
pleiotropy testing
id.exposure id.outcome outcome exposure egger_intercept se pval
Ae0Nt5 TcYOpY outcome exposure -0.0004771 0.0004298 0.2750741

Testing Outlier with PRESSO test

## $`Main MR results`
##        Exposure       MR Analysis Causal Estimate           Sd   T-stat
## 1 beta.exposure               Raw     0.005787622 0.0016045628 3.606978
## 2 beta.exposure Outlier-corrected     0.004639196 0.0009916789 4.678123
##        P-value
## 1 9.827571e-04
## 2 5.392219e-05
## 
## $`MR-PRESSO results`
## $`MR-PRESSO results`$`Global Test`
## $`MR-PRESSO results`$`Global Test`$RSSobs
## [1] 138.0242
## 
## $`MR-PRESSO results`$`Global Test`$Pvalue
## [1] "<0.001"
## 
## 
## $`MR-PRESSO results`$`Outlier Test`
##          RSSobs Pvalue
## 1  1.521081e-07      1
## 2  5.817698e-07      1
## 3  1.009412e-06      1
## 4  2.417938e-08      1
## 5  2.405264e-07      1
## 6  6.280592e-08      1
## 7  1.860700e-07      1
## 8  3.020725e-09      1
## 9  3.419849e-07      1
## 10 3.559686e-07      1
## 11 9.105534e-08      1
## 12 6.135183e-08      1
## 13 1.624695e-07      1
## 14 6.151788e-07      1
## 15 1.221771e-06  0.105
## 16 6.157827e-08      1
## 17 1.439327e-06 <0.035
## 18 1.753513e-07      1
## 19 3.837921e-08      1
## 20 3.905884e-06      1
## 21 9.285519e-06 <0.035
## 22 2.051024e-08      1
## 23 8.867844e-06 <0.035
## 24 4.106314e-08      1
## 25 6.460918e-08      1
## 26 3.992742e-09      1
## 27 2.082157e-07      1
## 28 1.062721e-07      1
## 29 1.867962e-06      1
## 30 1.306280e-07      1
## 31 6.780487e-08      1
## 32 4.822383e-08      1
## 33 2.477448e-07      1
## 34 2.927522e-07      1
## 35 1.914666e-07      1
## 
## $`MR-PRESSO results`$`Distortion Test`
## $`MR-PRESSO results`$`Distortion Test`$`Outliers Indices`
## [1] 17 21 23
## 
## $`MR-PRESSO results`$`Distortion Test`$`Distortion Coefficient`
## beta.exposure 
##      24.75486 
## 
## $`MR-PRESSO results`$`Distortion Test`$Pvalue
## [1] 0.118
## [1] "Four SNPs (rs59014134, rs75117471, rs115849089, and rs17092642) were detected by MRPRESSO and excluded for further analyses"
MR analysis after excluding SNPs detected by MRPRESSO
id.exposure id.outcome outcome exposure method nsnp b se pval
Ae0Nt5 TcYOpY outcome exposure MR Egger 31 0.0104860 0.0054383 0.0636786
Ae0Nt5 TcYOpY outcome exposure Weighted median 31 0.0044096 0.0013655 0.0012407
Ae0Nt5 TcYOpY outcome exposure Inverse variance weighted 31 0.0056432 0.0017519 0.0012771
Ae0Nt5 TcYOpY outcome exposure Simple mode 31 0.0039667 0.0027647 0.1616979
Ae0Nt5 TcYOpY outcome exposure Weighted mode 31 0.0063459 0.0020183 0.0037375

Heterogeneity testing
id.exposure id.outcome outcome exposure method Q Q_df Q_pval
Ae0Nt5 TcYOpY outcome exposure MR Egger 121.6015 29 0
Ae0Nt5 TcYOpY outcome exposure Inverse variance weighted 125.3132 30 0
pleiotropy testing
id.exposure id.outcome outcome exposure egger_intercept se pval
Ae0Nt5 TcYOpY outcome exposure -0.0004444 0.0004723 0.3545535

Radial test

## 
## Radial IVW
## 
##                     Estimate    Std.Error  t value     Pr(>|t|)
## Effect (Mod.2nd) 0.005791559 0.0016047538 3.609002 3.073776e-04
## Iterative        0.005791559 0.0016047538 3.609002 3.073776e-04
## Exact (FE)       0.006560284 0.0008407593 7.802808 6.054467e-15
## Exact (RE)       0.005996549 0.0015560471 3.853706 4.914767e-04
## 
## 
## Residual standard error: 1.921 on 34 degrees of freedom
## 
## F-statistic: 13.02 on 1 and 34 DF, p-value: 0.000977
## Q-Statistic for heterogeneity: 125.4644 on 34 DF , p-value: 2.088556e-12
## 
##  Outliers detected 
## Number of iterations = 2
##          SNP Q_statistic      p.value
## 1  rs2642636    11.60042 6.593689e-04
## 2   rs429358    40.64017 1.830054e-10
## 3 rs56289821    30.63685 3.111276e-08
## [1] "Three SNPs (rs2642636, rs429358, and rs56289821) were detected by Radial and excluded for further analyses"
MR analysis after excluding SNPs detected by MRPRESSO
id.exposure id.outcome outcome exposure method nsnp b se pval
Ae0Nt5 TcYOpY outcome exposure MR Egger 32 0.0087907 0.0029480 0.0056400
Ae0Nt5 TcYOpY outcome exposure Weighted median 32 0.0045552 0.0012944 0.0004327
Ae0Nt5 TcYOpY outcome exposure Inverse variance weighted 32 0.0046392 0.0009917 0.0000029
Ae0Nt5 TcYOpY outcome exposure Simple mode 32 0.0028732 0.0029038 0.3300998
Ae0Nt5 TcYOpY outcome exposure Weighted mode 32 0.0075955 0.0023215 0.0026235

Heterogeneity testing
id.exposure id.outcome outcome exposure method Q Q_df Q_pval
Ae0Nt5 TcYOpY outcome exposure MR Egger 39.76543 30 0.1094881
Ae0Nt5 TcYOpY outcome exposure Inverse variance weighted 42.71531 31 0.0784330
pleiotropy testing
id.exposure id.outcome outcome exposure egger_intercept se pval
Ae0Nt5 TcYOpY outcome exposure -0.0003872 0.0002596 0.1461938

Cook’s distance

In statistics, Cook’s distance or Cook’s D is a commonly used estimate of the influence of a data point when performing a least-squares regression analysis.[1] In a practical ordinary least squares analysis, Cook’s distance can be used in several ways:

1- To indicate influential data points that are particularly worth checking for validity.

2- To indicate regions of the design space where it would be good to be able to obtain more data points.

It is named after the American statistician R. Dennis Cook, who introduced the concept in 1977.

Refernce

Run After deleting new outlier: Final Results:

MR analysis after deleting outliers
id.exposure id.outcome outcome exposure method nsnp b se pval
Ae0Nt5 TcYOpY outcome exposure MR Egger 32 0.0087907 0.0029480 0.0056400
Ae0Nt5 TcYOpY outcome exposure Weighted median 32 0.0045552 0.0012803 0.0003739
Ae0Nt5 TcYOpY outcome exposure Inverse variance weighted 32 0.0046392 0.0009917 0.0000029
Ae0Nt5 TcYOpY outcome exposure Simple mode 32 0.0028732 0.0030813 0.3582952
Ae0Nt5 TcYOpY outcome exposure Weighted mode 32 0.0075955 0.0022451 0.0019571

Heterogeneity testing
id.exposure id.outcome outcome exposure method Q Q_df Q_pval
Ae0Nt5 TcYOpY outcome exposure MR Egger 39.76543 30 0.1094881
Ae0Nt5 TcYOpY outcome exposure Inverse variance weighted 42.71531 31 0.0784330
pleiotropy testing
id.exposure id.outcome outcome exposure egger_intercept se pval
Ae0Nt5 TcYOpY outcome exposure -0.0003872 0.0002596 0.1461938

Sensitivity analyses with MendelianRandomization Package

## 
## Inverse-variance weighted method
## (variants uncorrelated, random-effect model)
## 
## Number of Variants : 32 
## 
## ------------------------------------------------------------------
##  Method Estimate Std Error 95% CI       p-value
##     IVW    0.005     0.001 0.003, 0.007   0.000
## ------------------------------------------------------------------
## Residual standard error =  1.174 
## Heterogeneity test statistic (Cochran's Q) = 42.7153 on 31 degrees of freedom, (p-value = 0.0784). I^2 = 27.4%.
##                     Method Estimate Std Error 95% CI        P-value
##              Simple median    0.003     0.001   0.000 0.006   0.022
##            Weighted median    0.005     0.001   0.003 0.008   0.000
##  Penalized weighted median    0.006     0.001   0.004 0.009   0.000
##                                                                    
##                        IVW    0.005     0.001   0.003 0.007   0.000
##              Penalized IVW    0.005     0.001   0.003 0.007   0.000
##                 Robust IVW    0.005     0.001   0.003 0.007   0.000
##       Penalized robust IVW    0.005     0.001   0.003 0.007   0.000
##                                                                    
##                   MR-Egger    0.009     0.003   0.003 0.015   0.003
##                (intercept)    0.000     0.000  -0.001 0.000   0.136
##         Penalized MR-Egger    0.009     0.003   0.003 0.015   0.003
##                (intercept)    0.000     0.000  -0.001 0.000   0.136
##            Robust MR-Egger    0.009     0.003   0.003 0.016   0.006
##                (intercept)    0.000     0.000  -0.001 0.000   0.159
##  Penalized robust MR-Egger    0.009     0.003   0.003 0.016   0.006
##                (intercept)    0.000     0.000  -0.001 0.000   0.159

id.exposure id.outcome exposure outcome snp_r2.exposure snp_r2.outcome correct_causal_direction steiger_pval
Ae0Nt5 TcYOpY exposure outcome 0.0023928 0.0001476 TRUE 0
## $r2_exp
## [1] 0
## 
## $r2_out
## [1] 0.25
## 
## $r2_exp_adj
## [1] 0
## 
## $r2_out_adj
## [1] 0.25
## 
## $correct_causal_direction
## [1] FALSE
## 
## $steiger_test
## [1] 0
## 
## $correct_causal_direction_adj
## [1] FALSE
## 
## $steiger_test_adj
## [1] 0
## 
## $vz
## [1] NaN
## 
## $vz0
## [1] 0
## 
## $vz1
## [1] NaN
## 
## $sensitivity_ratio
## [1] NaN
## 
## $sensitivity_plot

Working with MRraps

## $beta.hat
## [1] 0.00484049
## 
## $beta.se
## [1] 0.000882532
## 
## $beta.p.value
## [1] 4.139957e-08
## 
## $naive.se
## [1] 0.0008690899
## 
## $chi.sq.test
## [1] 41.4272
##   over.dispersion loss.function    beta.hat      beta.se
## 1           FALSE            l2 0.004840490 0.0008825320
## 2           FALSE         huber 0.004956247 0.0009068622
## 3           FALSE         tukey 0.004999124 0.0009073923
## 4            TRUE            l2 0.004789447 0.0010042786
## 5            TRUE         huber 0.004852868 0.0010587245
## 6            TRUE         tukey 0.004864635 0.0010644772
## 
## Constrained maximum likelihood method (MRcML) 
## Number of Variants:  32 
## Results for:  cML-MA-BIC 
## ------------------------------------------------------------------
##      Method Estimate    SE Pvalue        95% CI
##  cML-MA-BIC    0.005 0.001  0.000 [0.003,0.007]
## ------------------------------------------------------------------
## 
## Debiased inverse-variance weighted method
## (Over.dispersion:TRUE)
## 
## Number of Variants : 32 
## ------------------------------------------------------------------
##  Method Estimate Std Error 95% CI       p-value Condition
##    dIVW    0.005     0.001 0.003, 0.007   0.000   174.427
## ------------------------------------------------------------------
## 
## Mode-based method of Hartwig et al
## (weighted, delta standard errors [not assuming NOME], bandwidth factor = 1)
## 
## Number of Variants : 32 
## ------------------------------------------------------------------
##  Method Estimate Std Error 95% CI       p-value
##     MBE    0.008     0.002 0.003, 0.012   0.000
## ------------------------------------------------------------------

[IHD]

Introduction

  • Title: Investigating the causality between Monounsaturated Fatty Acids on Cardiovascular Disease

Data Preparation

1- Number of total SNPs in exposure: 12,321,875 SNPs

2- Number of Selected SNPs exposure: 44 SNPs

3- Number of total SNPs in outcome: 13,586,589 SNPs

4- Number of common variants between exposure and outcome: 44 SNPs

5- Number of SNPs after harmonization (action=2) = 42 SNPs

6- Number of SNPs after removing HLA region with exploring in HLA Genes, Nomenclature = 42 SNPs

7- Number of SNPs after removing those that have MAF < 0.01 = 42 SNPs

8- Checking pleiotropy by PhenoScanner:

How many SNPs have been eliminated after checking the PhenoScanner website: 4 SNPs (rs429358, rs56289821, and rs964184)

Checking weakness of the instruments

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   21.29   22.20   24.82   29.35   27.70   81.06

How many SNPs have been eliminated with checking the weakness: 0 SNP

RUN an initial MR:

Initial MR analysis
id.exposure id.outcome outcome exposure method nsnp b se pval
AyPdJL f31Mp6 outcome exposure MR Egger 39 0.0050467 0.0044966 0.2689503
AyPdJL f31Mp6 outcome exposure Weighted median 39 0.0041414 0.0021303 0.0518906
AyPdJL f31Mp6 outcome exposure Inverse variance weighted 39 0.0063470 0.0017815 0.0003671
AyPdJL f31Mp6 outcome exposure Simple mode 39 0.0002188 0.0045634 0.9620027
AyPdJL f31Mp6 outcome exposure Weighted mode 39 0.0003692 0.0049426 0.9408443

Heterogeneity testing
id.exposure id.outcome outcome exposure method Q Q_df Q_pval
AyPdJL f31Mp6 outcome exposure MR Egger 73.64755 37 0.0003178
AyPdJL f31Mp6 outcome exposure Inverse variance weighted 73.84589 38 0.0004383
pleiotropy testing
id.exposure id.outcome outcome exposure egger_intercept se pval
AyPdJL f31Mp6 outcome exposure 0.0001302 0.0004124 0.7540298

Testing Outlier with PRESSO test

## $`Main MR results`
##        Exposure       MR Analysis Causal Estimate          Sd   T-stat
## 1 beta.exposure               Raw     0.006346974 0.001781519 3.562676
## 2 beta.exposure Outlier-corrected     0.005401467 0.001630537 3.312691
##       P-value
## 1 0.001008592
## 2 0.002072496
## 
## $`MR-PRESSO results`
## $`MR-PRESSO results`$`Global Test`
## $`MR-PRESSO results`$`Global Test`$RSSobs
## [1] 78.32892
## 
## $`MR-PRESSO results`$`Global Test`$Pvalue
## [1] "<0.001"
## 
## 
## $`MR-PRESSO results`$`Outlier Test`
##          RSSobs Pvalue
## 1  7.589045e-09      1
## 2  1.520959e-07      1
## 3  1.195763e-05      1
## 4  1.151350e-05 <0.039
## 5  1.315259e-05      1
## 6  1.829718e-08      1
## 7  3.177484e-06  0.546
## 8  7.762960e-07      1
## 9  2.255390e-07      1
## 10 6.914358e-07      1
## 11 6.033486e-07      1
## 12 2.501580e-07      1
## 13 1.045150e-06      1
## 14 3.219794e-05      1
## 15 2.531421e-06  0.117
## 16 1.119834e-06      1
## 17 1.536286e-07      1
## 18 2.737095e-07      1
## 19 1.442225e-06      1
## 20 1.196424e-06      1
## 21 1.358017e-08      1
## 22 8.712847e-07      1
## 23 5.256833e-07      1
## 24 1.713336e-08      1
## 25 8.242892e-06      1
## 26 1.273851e-07      1
## 27 2.723757e-06      1
## 28 2.269390e-06  0.702
## 29 7.465580e-08      1
## 30 1.582110e-07      1
## 31 6.197990e-08      1
## 32 2.102623e-07      1
## 33 4.351909e-06      1
## 34 3.165556e-06      1
## 35 1.212979e-06      1
## 36 3.320494e-06      1
## 37 1.093058e-07      1
## 38 1.275663e-07      1
## 39 6.704272e-07      1
## 
## $`MR-PRESSO results`$`Distortion Test`
## $`MR-PRESSO results`$`Distortion Test`$`Outliers Indices`
## [1] 4
## 
## $`MR-PRESSO results`$`Distortion Test`$`Distortion Coefficient`
## beta.exposure 
##      17.50465 
## 
## $`MR-PRESSO results`$`Distortion Test`$Pvalue
## [1] 0.471
## [1] "One SNP (rs115849089) were detected by MRPRESSO and excluded for further analyses"
MR analysis after excluding SNPs detected by MRPRESSO
id.exposure id.outcome outcome exposure method nsnp b se pval
AyPdJL f31Mp6 outcome exposure MR Egger 38 0.0032148 0.0040745 0.4352741
AyPdJL f31Mp6 outcome exposure Weighted median 38 0.0040640 0.0021087 0.0539520
AyPdJL f31Mp6 outcome exposure Inverse variance weighted 38 0.0054015 0.0016305 0.0009240
AyPdJL f31Mp6 outcome exposure Simple mode 38 0.0003045 0.0045716 0.9472453
AyPdJL f31Mp6 outcome exposure Weighted mode 38 0.0004557 0.0052850 0.9317594

Heterogeneity testing
id.exposure id.outcome outcome exposure method Q Q_df Q_pval
AyPdJL f31Mp6 outcome exposure MR Egger 57.64511 36 0.0124632
AyPdJL f31Mp6 outcome exposure Inverse variance weighted 58.19616 37 0.0145811
pleiotropy testing
id.exposure id.outcome outcome exposure egger_intercept se pval
AyPdJL f31Mp6 outcome exposure 0.0002176 0.0003709 0.5611136

Radial test

## 
## Radial IVW
## 
##                     Estimate   Std.Error  t value     Pr(>|t|)
## Effect (Mod.2nd) 0.006372348 0.001783352 3.573243 3.525878e-04
## Iterative        0.006372348 0.001783352 3.573243 3.525878e-04
## Exact (FE)       0.006807760 0.001295684 5.254183 1.486830e-07
## Exact (RE)       0.006573021 0.001994518 3.295543 2.134160e-03
## 
## 
## Residual standard error: 1.379 on 38 degrees of freedom
## 
## F-statistic: 12.77 on 1 and 38 DF, p-value: 0.000979
## Q-Statistic for heterogeneity: 72.24359 on 38 DF , p-value: 0.000669887
## 
##  Outliers detected 
## Number of iterations = 2
##           SNP Q_statistic      p.value
## 1 rs115849089    14.75908 0.0001221577
## [1] "One SNP (rs115849089) were detected by Radial and excluded for further analyses"
MR analysis after excluding SNPs detected by MRPRESSO
id.exposure id.outcome outcome exposure method nsnp b se pval
AyPdJL f31Mp6 outcome exposure MR Egger 38 0.0032148 0.0040745 0.4352741
AyPdJL f31Mp6 outcome exposure Weighted median 38 0.0040640 0.0020613 0.0486539
AyPdJL f31Mp6 outcome exposure Inverse variance weighted 38 0.0054015 0.0016305 0.0009240
AyPdJL f31Mp6 outcome exposure Simple mode 38 0.0003045 0.0045575 0.9470827
AyPdJL f31Mp6 outcome exposure Weighted mode 38 0.0004557 0.0047734 0.9244664

Heterogeneity testing
id.exposure id.outcome outcome exposure method Q Q_df Q_pval
AyPdJL f31Mp6 outcome exposure MR Egger 57.64511 36 0.0124632
AyPdJL f31Mp6 outcome exposure Inverse variance weighted 58.19616 37 0.0145811
pleiotropy testing
id.exposure id.outcome outcome exposure egger_intercept se pval
AyPdJL f31Mp6 outcome exposure 0.0002176 0.0003709 0.5611136

Cook’s distance

In statistics, Cook’s distance or Cook’s D is a commonly used estimate of the influence of a data point when performing a least-squares regression analysis.[1] In a practical ordinary least squares analysis, Cook’s distance can be used in several ways:

1- To indicate influential data points that are particularly worth checking for validity.

2- To indicate regions of the design space where it would be good to be able to obtain more data points.

It is named after the American statistician R. Dennis Cook, who introduced the concept in 1977.

Refernce

Run After deleting new outlier: Final Results:

MR analysis after deleting outliers
id.exposure id.outcome outcome exposure method nsnp b se pval
AyPdJL f31Mp6 outcome exposure MR Egger 36 0.0034307 0.0036092 0.3485341
AyPdJL f31Mp6 outcome exposure Weighted median 36 0.0029611 0.0021228 0.1630418
AyPdJL f31Mp6 outcome exposure Inverse variance weighted 36 0.0041525 0.0014793 0.0049989
AyPdJL f31Mp6 outcome exposure Simple mode 36 0.0000657 0.0046212 0.9887343
AyPdJL f31Mp6 outcome exposure Weighted mode 36 0.0002129 0.0050532 0.9666373

Heterogeneity testing
id.exposure id.outcome outcome exposure method Q Q_df Q_pval
AyPdJL f31Mp6 outcome exposure MR Egger 42.69331 34 0.1456808
AyPdJL f31Mp6 outcome exposure Inverse variance weighted 42.75402 35 0.1724731
pleiotropy testing
id.exposure id.outcome outcome exposure egger_intercept se pval
AyPdJL f31Mp6 outcome exposure 7.28e-05 0.0003312 0.8272782

Sensitivity analyses with MendelianRandomization Package

## 
## Inverse-variance weighted method
## (variants uncorrelated, random-effect model)
## 
## Number of Variants : 36 
## 
## ------------------------------------------------------------------
##  Method Estimate Std Error 95% CI       p-value
##     IVW    0.004     0.001 0.001, 0.007   0.005
## ------------------------------------------------------------------
## Residual standard error =  1.105 
## Heterogeneity test statistic (Cochran's Q) = 42.7540 on 35 degrees of freedom, (p-value = 0.1725). I^2 = 18.1%.
##                     Method Estimate Std Error 95% CI        P-value
##              Simple median    0.002     0.002  -0.002 0.006   0.306
##            Weighted median    0.004     0.002   0.000 0.008   0.070
##  Penalized weighted median    0.003     0.002  -0.001 0.007   0.195
##                                                                    
##                        IVW    0.004     0.001   0.001 0.007   0.005
##              Penalized IVW    0.004     0.001   0.001 0.007   0.005
##                 Robust IVW    0.004     0.002   0.000 0.007   0.036
##       Penalized robust IVW    0.004     0.002   0.000 0.007   0.036
##                                                                    
##                   MR-Egger    0.003     0.004  -0.004 0.011   0.342
##                (intercept)    0.000     0.000  -0.001 0.001   0.826
##         Penalized MR-Egger    0.003     0.004  -0.004 0.011   0.342
##                (intercept)    0.000     0.000  -0.001 0.001   0.826
##            Robust MR-Egger    0.003     0.004  -0.006 0.011   0.532
##                (intercept)    0.000     0.000  -0.001 0.001   0.756
##  Penalized robust MR-Egger    0.003     0.004  -0.006 0.011   0.532
##                (intercept)    0.000     0.000  -0.001 0.001   0.756

id.exposure id.outcome exposure outcome snp_r2.exposure snp_r2.outcome correct_causal_direction steiger_pval
AyPdJL f31Mp6 exposure outcome 0.0024037 0.0001059 TRUE 0
## $r2_exp
## [1] 0
## 
## $r2_out
## [1] 0.25
## 
## $r2_exp_adj
## [1] 0
## 
## $r2_out_adj
## [1] 0.25
## 
## $correct_causal_direction
## [1] FALSE
## 
## $steiger_test
## [1] 0
## 
## $correct_causal_direction_adj
## [1] FALSE
## 
## $steiger_test_adj
## [1] 0
## 
## $vz
## [1] NaN
## 
## $vz0
## [1] 0
## 
## $vz1
## [1] NaN
## 
## $sensitivity_ratio
## [1] NaN
## 
## $sensitivity_plot

Working with MRraps

## $beta.hat
## [1] 0.004338291
## 
## $beta.se
## [1] 0.001395069
## 
## $beta.p.value
## [1] 0.001872575
## 
## $naive.se
## [1] 0.001370345
## 
## $chi.sq.test
## [1] 42.34696
##   over.dispersion loss.function    beta.hat     beta.se
## 1           FALSE            l2 0.004338291 0.001395069
## 2           FALSE         huber 0.003551043 0.001425995
## 3           FALSE         tukey 0.003792444 0.001427516
## 4            TRUE            l2 0.004144624 0.001487892
## 5            TRUE         huber 0.003407176 0.001580644
## 6            TRUE         tukey 0.003600889 0.001589118
## 
## MR-Lasso method 
## 
## Number of variants : 36 
## Number of valid instruments : 33 
## Tuning parameter : 0.3418043 
## ------------------------------------------------------------------
##  Exposure Estimate Std Error  95% CI       p-value
##  exposure    0.002     0.001 -0.001, 0.005   0.197
## ------------------------------------------------------------------
## 
## Constrained maximum likelihood method (MRcML) 
## Number of Variants:  36 
## Results for:  cML-MA-BIC 
## ------------------------------------------------------------------
##      Method Estimate    SE Pvalue        95% CI
##  cML-MA-BIC    0.004 0.001  0.002 [0.002,0.007]
## ------------------------------------------------------------------
## 
## Debiased inverse-variance weighted method
## (Over.dispersion:TRUE)
## 
## Number of Variants : 36 
## ------------------------------------------------------------------
##  Method Estimate Std Error 95% CI       p-value Condition
##    dIVW    0.004     0.002 0.001, 0.007   0.005   164.553
## ------------------------------------------------------------------
## 
## Mode-based method of Hartwig et al
## (weighted, delta standard errors [not assuming NOME], bandwidth factor = 1)
## 
## Number of Variants : 36 
## ------------------------------------------------------------------
##  Method Estimate Std Error  95% CI       p-value
##     MBE    0.000     0.005 -0.010, 0.011   0.968
## ------------------------------------------------------------------

[MI]

Introduction

  • Title: Investigating the causality between Monounsaturated Fatty Acids on Cardiovascular Disease

Data Preparation

1- Number of total SNPs in exposure: 12,321,875 SNPs

2- Number of Selected SNPs exposure: 44 SNPs

3- Number of total SNPs in outcome: 9,851,867 SNPs

4- Number of common variants between exposure and outcome: 34 SNPs

5- Number of SNPs after harmonization (action=2) = 33 SNPs

6- Number of SNPs after removing HLA region with exploring in HLA Genes, Nomenclature = 33 SNPs

7- Number of SNPs after removing those that have MAF < 0.01 = 33 SNPs

8- Checking pleiotropy by PhenoScanner:

How many SNPs have been eliminated after checking the PhenoScanner website: 4 SNPs (rs429358, rs429358, rs56289821, and rs964184)

Checking weakness of the instruments

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   21.34   22.52   24.92   30.36   27.97   86.31

How many SNPs have been eliminated with checking the weakness: 0 SNP

RUN an initial MR:

Initial MR analysis
id.exposure id.outcome outcome exposure method nsnp b se pval
R5oDLI pjYnfY outcome exposure MR Egger 30 0.0047384 0.0034165 0.1764078
R5oDLI pjYnfY outcome exposure Weighted median 30 0.0015343 0.0012566 0.2220773
R5oDLI pjYnfY outcome exposure Inverse variance weighted 30 0.0017718 0.0009866 0.0725214
R5oDLI pjYnfY outcome exposure Simple mode 30 0.0015958 0.0026884 0.5573972
R5oDLI pjYnfY outcome exposure Weighted mode 30 0.0018886 0.0022402 0.4061129

Heterogeneity testing
id.exposure id.outcome outcome exposure method Q Q_df Q_pval
R5oDLI pjYnfY outcome exposure MR Egger 39.33190 28 0.0757304
R5oDLI pjYnfY outcome exposure Inverse variance weighted 40.48806 29 0.0762678
pleiotropy testing
id.exposure id.outcome outcome exposure egger_intercept se pval
R5oDLI pjYnfY outcome exposure -0.0002567 0.000283 0.3720285

Testing Outlier with PRESSO test

## $`Main MR results`
##        Exposure       MR Analysis Causal Estimate           Sd   T-stat
## 1 beta.exposure               Raw     0.001771766 0.0009865994 1.795831
## 2 beta.exposure Outlier-corrected              NA           NA       NA
##      P-value
## 1 0.08294832
## 2         NA
## 
## $`MR-PRESSO results`
## $`MR-PRESSO results`$`Global Test`
## $`MR-PRESSO results`$`Global Test`$RSSobs
## [1] 43.4608
## 
## $`MR-PRESSO results`$`Global Test`$Pvalue
## [1] 0.085
MR analysis after excluding SNPs detected by MRPRESSO
id.exposure id.outcome outcome exposure method nsnp b se pval
R5oDLI pjYnfY outcome exposure MR Egger 30 0.0047384 0.0034165 0.1764078
R5oDLI pjYnfY outcome exposure Weighted median 30 0.0015343 0.0012695 0.2268038
R5oDLI pjYnfY outcome exposure Inverse variance weighted 30 0.0017718 0.0009866 0.0725214
R5oDLI pjYnfY outcome exposure Simple mode 30 0.0015958 0.0026708 0.5548211
R5oDLI pjYnfY outcome exposure Weighted mode 30 0.0018886 0.0020249 0.3586752

Heterogeneity testing
id.exposure id.outcome outcome exposure method Q Q_df Q_pval
R5oDLI pjYnfY outcome exposure MR Egger 39.33190 28 0.0757304
R5oDLI pjYnfY outcome exposure Inverse variance weighted 40.48806 29 0.0762678
pleiotropy testing
id.exposure id.outcome outcome exposure egger_intercept se pval
R5oDLI pjYnfY outcome exposure -0.0002567 0.000283 0.3720285

Radial test

## 
## Radial IVW
## 
##                     Estimate    Std.Error  t value   Pr(>|t|)
## Effect (Mod.2nd) 0.001771628 0.0009866445 1.795610 0.07255661
## Iterative        0.001771628 0.0009866445 1.795610 0.07255661
## Exact (FE)       0.001863303 0.0008373257 2.225302 0.02606098
## Exact (RE)       0.001838722 0.0010371981 1.772778 0.08677105
## 
## 
## Residual standard error: 1.179 on 29 degrees of freedom
## 
## F-statistic: 3.22 on 1 and 29 DF, p-value: 0.083
## Q-Statistic for heterogeneity: 40.28686 on 29 DF , p-value: 0.07935495
## 
##  No significant outliers 
## Number of iterations = 2
## [1] "No significant outliers"
MR analysis after excluding SNPs detected by MRPRESSO
id.exposure id.outcome outcome exposure method nsnp b se pval
R5oDLI pjYnfY outcome exposure MR Egger 30 0.0047384 0.0034165 0.1764078
R5oDLI pjYnfY outcome exposure Weighted median 30 0.0015343 0.0012175 0.2075762
R5oDLI pjYnfY outcome exposure Inverse variance weighted 30 0.0017718 0.0009866 0.0725214
R5oDLI pjYnfY outcome exposure Simple mode 30 0.0015958 0.0026429 0.5506837
R5oDLI pjYnfY outcome exposure Weighted mode 30 0.0018886 0.0020965 0.3751116

Heterogeneity testing
id.exposure id.outcome outcome exposure method Q Q_df Q_pval
R5oDLI pjYnfY outcome exposure MR Egger 39.33190 28 0.0757304
R5oDLI pjYnfY outcome exposure Inverse variance weighted 40.48806 29 0.0762678
pleiotropy testing
id.exposure id.outcome outcome exposure egger_intercept se pval
R5oDLI pjYnfY outcome exposure -0.0002567 0.000283 0.3720285

Cook’s distance

In statistics, Cook’s distance or Cook’s D is a commonly used estimate of the influence of a data point when performing a least-squares regression analysis.[1] In a practical ordinary least squares analysis, Cook’s distance can be used in several ways:

1- To indicate influential data points that are particularly worth checking for validity.

2- To indicate regions of the design space where it would be good to be able to obtain more data points.

It is named after the American statistician R. Dennis Cook, who introduced the concept in 1977.

Refernce

Run After deleting new outlier: Final Results:

MR analysis after deleting outliers
id.exposure id.outcome outcome exposure method nsnp b se pval
R5oDLI pjYnfY outcome exposure MR Egger 27 0.0050723 0.0030927 0.1135130
R5oDLI pjYnfY outcome exposure Weighted median 27 0.0013964 0.0013041 0.2842530
R5oDLI pjYnfY outcome exposure Inverse variance weighted 27 0.0011386 0.0008867 0.1990822
R5oDLI pjYnfY outcome exposure Simple mode 27 0.0014728 0.0025957 0.5753012
R5oDLI pjYnfY outcome exposure Weighted mode 27 0.0017779 0.0022230 0.4310874

Heterogeneity testing
id.exposure id.outcome outcome exposure method Q Q_df Q_pval
R5oDLI pjYnfY outcome exposure MR Egger 21.26795 25 0.6775772
R5oDLI pjYnfY outcome exposure Inverse variance weighted 23.03059 26 0.6312158
pleiotropy testing
id.exposure id.outcome outcome exposure egger_intercept se pval
R5oDLI pjYnfY outcome exposure -0.0003332 0.000251 0.1962922

Sensitivity analyses with MendelianRandomization Package

## 
## Inverse-variance weighted method
## (variants uncorrelated, random-effect model)
## 
## Number of Variants : 27 
## 
## ------------------------------------------------------------------
##  Method Estimate Std Error  95% CI       p-value
##     IVW    0.001     0.001 -0.001, 0.003   0.199
## ------------------------------------------------------------------
## Residual standard error =  0.941 
## Residual standard error is set to 1 in calculation of confidence interval when its estimate is less than 1.
## Heterogeneity test statistic (Cochran's Q) = 23.0306 on 26 degrees of freedom, (p-value = 0.6312). I^2 = 0.0%.
##                     Method Estimate Std Error 95% CI        P-value
##              Simple median    0.001     0.001  -0.001 0.004   0.339
##            Weighted median    0.001     0.001  -0.001 0.004   0.269
##  Penalized weighted median    0.001     0.001  -0.001 0.004   0.269
##                                                                    
##                        IVW    0.001     0.001  -0.001 0.003   0.199
##              Penalized IVW    0.001     0.001  -0.001 0.003   0.199
##                 Robust IVW    0.001     0.001  -0.001 0.003   0.187
##       Penalized robust IVW    0.001     0.001  -0.001 0.003   0.187
##                                                                    
##                   MR-Egger    0.005     0.003  -0.001 0.011   0.101
##                (intercept)    0.000     0.000  -0.001 0.000   0.184
##         Penalized MR-Egger    0.005     0.003  -0.001 0.011   0.101
##                (intercept)    0.000     0.000  -0.001 0.000   0.184
##            Robust MR-Egger    0.005     0.002   0.001 0.010   0.029
##                (intercept)    0.000     0.000  -0.001 0.000   0.096
##  Penalized robust MR-Egger    0.005     0.002   0.001 0.010   0.029
##                (intercept)    0.000     0.000  -0.001 0.000   0.096

id.exposure id.outcome exposure outcome snp_r2.exposure snp_r2.outcome correct_causal_direction steiger_pval
R5oDLI pjYnfY exposure outcome 0.0019071 4.99e-05 TRUE 0
## $r2_exp
## [1] 0
## 
## $r2_out
## [1] 0.25
## 
## $r2_exp_adj
## [1] 0
## 
## $r2_out_adj
## [1] 0.25
## 
## $correct_causal_direction
## [1] FALSE
## 
## $steiger_test
## [1] 0
## 
## $correct_causal_direction_adj
## [1] FALSE
## 
## $steiger_test_adj
## [1] 0
## 
## $vz
## [1] NaN
## 
## $vz0
## [1] 0
## 
## $vz1
## [1] NaN
## 
## $sensitivity_ratio
## [1] NaN
## 
## $sensitivity_plot

Working with MRraps

## $beta.hat
## [1] 0.001171598
## 
## $beta.se
## [1] 0.0009206665
## 
## $beta.p.value
## [1] 0.2031764
## 
## $naive.se
## [1] 0.0009051455
## 
## $chi.sq.test
## [1] 22.98271
##   over.dispersion loss.function    beta.hat      beta.se
## 1           FALSE            l2 0.001171598 0.0009206665
## 2           FALSE         huber 0.001259075 0.0009449070
## 3           FALSE         tukey 0.001207582 0.0009447155
## 4            TRUE            l2 0.001173555 0.0009415467
## 5            TRUE         huber 0.001249328 0.0009449544
## 6            TRUE         tukey 0.001205204 0.0009447884
## 
## MR-Lasso method 
## 
## Number of variants : 27 
## Number of valid instruments : 27 
## Tuning parameter : 0.3447026 
## ------------------------------------------------------------------
##  Exposure Estimate Std Error  95% CI       p-value
##  exposure    0.001     0.001 -0.001, 0.003   0.199
## ------------------------------------------------------------------
## 
## Constrained maximum likelihood method (MRcML) 
## Number of Variants:  27 
## Results for:  cML-MA-BIC 
## ------------------------------------------------------------------
##      Method Estimate    SE Pvalue         95% CI
##  cML-MA-BIC    0.001 0.001  0.193 [-0.001,0.003]
## ------------------------------------------------------------------
## 
## Debiased inverse-variance weighted method
## (Over.dispersion:TRUE)
## 
## Number of Variants : 27 
## ------------------------------------------------------------------
##  Method Estimate Std Error  95% CI       p-value Condition
##    dIVW    0.001     0.001 -0.001, 0.003   0.200   151.059
## ------------------------------------------------------------------
## 
## Mode-based method of Hartwig et al
## (weighted, delta standard errors [not assuming NOME], bandwidth factor = 1)
## 
## Number of Variants : 27 
## ------------------------------------------------------------------
##  Method Estimate Std Error  95% CI       p-value
##     MBE    0.002     0.002 -0.003, 0.006   0.424
## ------------------------------------------------------------------

[HTN]

Introduction

  • Title: Investigating the causality between Monounsaturated Fatty Acids on Cardiovascular Disease

Data Preparation

1- Number of total SNPs in exposure: 12,321,875 SNPs

2- Number of Selected SNPs exposure: 44 SNPs

3- Number of total SNPs in outcome: 9,851,867 SNPs

4- Number of common variants between exposure and outcome: 40 SNPs

5- Number of SNPs after harmonization (action=2) = 40 SNPs

6- Number of SNPs after removing HLA region with exploring in HLA Genes, Nomenclature = 40 SNPs

7- Number of SNPs after removing those that have MAF < 0.01 = 40 SNPs

8- Checking pleiotropy by PhenoScanner:

How many SNPs have been eliminated after checking the PhenoScanner website: 4 SNPs (rs1554903 and rs429358)

Checking weakness of the instruments

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   21.29   22.26   24.01   30.47   28.10   86.31

How many SNPs have been eliminated with checking the weakness: 0 SNP

RUN an initial MR:

Initial MR analysis
id.exposure id.outcome outcome exposure method nsnp b se pval
fAazZl uqi37M outcome exposure MR Egger 37 0.0063402 0.0092623 0.4981580
fAazZl uqi37M outcome exposure Weighted median 37 0.0087999 0.0033911 0.0094601
fAazZl uqi37M outcome exposure Inverse variance weighted 37 0.0064439 0.0033897 0.0572976
fAazZl uqi37M outcome exposure Simple mode 37 0.0108348 0.0076165 0.1634740
fAazZl uqi37M outcome exposure Weighted mode 37 0.0102740 0.0060846 0.0999577

Heterogeneity testing
id.exposure id.outcome outcome exposure method Q Q_df Q_pval
fAazZl uqi37M outcome exposure MR Egger 86.47991 35 3.0e-06
fAazZl uqi37M outcome exposure Inverse variance weighted 86.48027 36 4.9e-06
pleiotropy testing
id.exposure id.outcome outcome exposure egger_intercept se pval
fAazZl uqi37M outcome exposure 1.01e-05 0.000837 0.9904535

Testing Outlier with PRESSO test

## $`Main MR results`
##        Exposure       MR Analysis Causal Estimate          Sd   T-stat
## 1 beta.exposure               Raw     0.006443858 0.003389660 1.901034
## 2 beta.exposure Outlier-corrected     0.006519442 0.003024166 2.155782
##      P-value
## 1 0.06532639
## 2 0.03826639
## 
## $`MR-PRESSO results`
## $`MR-PRESSO results`$`Global Test`
## $`MR-PRESSO results`$`Global Test`$RSSobs
## [1] 91.98975
## 
## $`MR-PRESSO results`$`Global Test`$Pvalue
## [1] "<0.001"
## 
## 
## $`MR-PRESSO results`$`Outlier Test`
##          RSSobs Pvalue
## 1  4.490365e-08      1
## 2  1.714504e-06      1
## 3  2.638681e-06      1
## 4  4.078232e-05      1
## 5  2.091918e-08      1
## 6  9.352604e-07      1
## 7  1.025229e-06      1
## 8  5.783611e-06   0.37
## 9  9.252651e-07      1
## 10 6.287315e-05      1
## 11 3.280347e-08      1
## 12 2.601647e-07      1
## 13 8.342274e-07      1
## 14 9.509238e-07      1
## 15 4.911202e-06      1
## 16 3.216041e-06      1
## 17 2.075340e-07      1
## 18 1.944242e-07      1
## 19 3.563012e-08      1
## 20 5.965255e-08      1
## 21 4.735677e-05  0.444
## 22 8.391620e-07      1
## 23 3.322211e-06      1
## 24 2.996330e-05      1
## 25 4.582138e-08      1
## 26 3.658378e-06      1
## 27 2.282894e-06      1
## 28 2.723694e-05 <0.037
## 29 4.140334e-06  0.999
## 30 2.527450e-05      1
## 31 1.641552e-05      1
## 32 1.591477e-08      1
## 33 3.129629e-06      1
## 34 2.413713e-07      1
## 35 4.193323e-05 <0.037
## 36 3.043937e-06      1
## 37 1.444488e-05  0.481
## 
## $`MR-PRESSO results`$`Distortion Test`
## $`MR-PRESSO results`$`Distortion Test`$`Outliers Indices`
## [1] 28 35
## 
## $`MR-PRESSO results`$`Distortion Test`$`Distortion Coefficient`
## beta.exposure 
##     -1.159357 
## 
## $`MR-PRESSO results`$`Distortion Test`$Pvalue
## [1] 0.968
MR analysis after excluding SNPs detected by MRPRESSO
id.exposure id.outcome outcome exposure method nsnp b se pval
fAazZl uqi37M outcome exposure MR Egger 36 0.0062364 0.0096263 0.5214344
fAazZl uqi37M outcome exposure Weighted median 36 0.0089921 0.0037121 0.0154201
fAazZl uqi37M outcome exposure Inverse variance weighted 36 0.0064117 0.0035025 0.0671570
fAazZl uqi37M outcome exposure Simple mode 36 0.0116985 0.0077081 0.1380716
fAazZl uqi37M outcome exposure Weighted mode 36 0.0108538 0.0062039 0.0889681

Heterogeneity testing
id.exposure id.outcome outcome exposure method Q Q_df Q_pval
fAazZl uqi37M outcome exposure MR Egger 86.47362 34 1.9e-06
fAazZl uqi37M outcome exposure Inverse variance weighted 86.47460 35 3.0e-06
pleiotropy testing
id.exposure id.outcome outcome exposure egger_intercept se pval
fAazZl uqi37M outcome exposure 1.69e-05 0.00086 0.9844792

Radial test

## 
## Radial IVW
## 
##                     Estimate   Std.Error  t value    Pr(>|t|)
## Effect (Mod.2nd) 0.006446794 0.003390225 1.901583 0.057225701
## Iterative        0.006446794 0.003390225 1.901583 0.057225701
## Exact (FE)       0.006990333 0.002197330 3.181285 0.001466233
## Exact (RE)       0.006675048 0.003642112 1.832741 0.075122185
## 
## 
## Residual standard error: 1.544 on 36 degrees of freedom
## 
## F-statistic: 3.62 on 1 and 36 DF, p-value: 0.0653
## Q-Statistic for heterogeneity: 85.81857 on 36 DF , p-value: 5.975782e-06
## 
##  Outliers detected 
## Number of iterations = 2
##         SNP Q_statistic      p.value
## 1 rs7123454     12.7942 0.0003476959
## 2 rs8107974     13.0189 0.0003083633
MR analysis after excluding SNPs detected by MRPRESSO
id.exposure id.outcome outcome exposure method nsnp b se pval
fAazZl uqi37M outcome exposure MR Egger 35 0.0082727 0.0082800 0.3250118
fAazZl uqi37M outcome exposure Weighted median 35 0.0088240 0.0035685 0.0134082
fAazZl uqi37M outcome exposure Inverse variance weighted 35 0.0065194 0.0030242 0.0311007
fAazZl uqi37M outcome exposure Simple mode 35 0.0108836 0.0072360 0.1417916
fAazZl uqi37M outcome exposure Weighted mode 35 0.0099036 0.0061075 0.1141422

Heterogeneity testing
id.exposure id.outcome outcome exposure method Q Q_df Q_pval
fAazZl uqi37M outcome exposure MR Egger 60.37413 33 0.0025134
fAazZl uqi37M outcome exposure Inverse variance weighted 60.46920 34 0.0034450
pleiotropy testing
id.exposure id.outcome outcome exposure egger_intercept se pval
fAazZl uqi37M outcome exposure -0.0001673 0.0007338 0.8210859

Cook’s distance

In statistics, Cook’s distance or Cook’s D is a commonly used estimate of the influence of a data point when performing a least-squares regression analysis.[1] In a practical ordinary least squares analysis, Cook’s distance can be used in several ways:

1- To indicate influential data points that are particularly worth checking for validity.

2- To indicate regions of the design space where it would be good to be able to obtain more data points.

It is named after the American statistician R. Dennis Cook, who introduced the concept in 1977.

Refernce

Run After deleting new outlier: Final Results:

MR analysis after deleting outliers
id.exposure id.outcome outcome exposure method nsnp b se pval
fAazZl uqi37M outcome exposure MR Egger 34 0.0026933 0.0082760 0.7469735
fAazZl uqi37M outcome exposure Weighted median 34 0.0082770 0.0035509 0.0197573
fAazZl uqi37M outcome exposure Inverse variance weighted 34 0.0048753 0.0029682 0.1004810
fAazZl uqi37M outcome exposure Simple mode 34 0.0107320 0.0068367 0.1260113
fAazZl uqi37M outcome exposure Weighted mode 34 0.0097417 0.0054812 0.0847364

Heterogeneity testing
id.exposure id.outcome outcome exposure method Q Q_df Q_pval
fAazZl uqi37M outcome exposure MR Egger 52.74506 32 0.0119122
fAazZl uqi37M outcome exposure Inverse variance weighted 52.87712 33 0.0155079
pleiotropy testing
id.exposure id.outcome outcome exposure egger_intercept se pval
fAazZl uqi37M outcome exposure 0.0002031 0.0007175 0.7789617

Sensitivity analyses with MendelianRandomization Package

## 
## Inverse-variance weighted method
## (variants uncorrelated, random-effect model)
## 
## Number of Variants : 34 
## 
## ------------------------------------------------------------------
##  Method Estimate Std Error  95% CI       p-value
##     IVW    0.005     0.003 -0.001, 0.011   0.100
## ------------------------------------------------------------------
## Residual standard error =  1.266 
## Heterogeneity test statistic (Cochran's Q) = 52.8771 on 33 degrees of freedom, (p-value = 0.0155). I^2 = 37.6%.
##                     Method Estimate Std Error 95% CI        P-value
##              Simple median    0.008     0.004   0.001 0.015   0.030
##            Weighted median    0.009     0.004   0.001 0.016   0.019
##  Penalized weighted median    0.009     0.004   0.002 0.016   0.014
##                                                                    
##                        IVW    0.005     0.003  -0.001 0.011   0.100
##              Penalized IVW    0.005     0.003  -0.001 0.011   0.100
##                 Robust IVW    0.005     0.003  -0.001 0.011   0.090
##       Penalized robust IVW    0.005     0.003  -0.001 0.011   0.090
##                                                                    
##                   MR-Egger    0.003     0.008  -0.014 0.019   0.745
##                (intercept)    0.000     0.001  -0.001 0.002   0.777
##         Penalized MR-Egger    0.003     0.008  -0.014 0.019   0.745
##                (intercept)    0.000     0.001  -0.001 0.002   0.777
##            Robust MR-Egger    0.003     0.011  -0.018 0.024   0.775
##                (intercept)    0.000     0.001  -0.002 0.002   0.836
##  Penalized robust MR-Egger    0.003     0.011  -0.018 0.024   0.775
##                (intercept)    0.000     0.001  -0.002 0.002   0.836

id.exposure id.outcome exposure outcome snp_r2.exposure snp_r2.outcome correct_causal_direction steiger_pval
fAazZl uqi37M exposure outcome 0.0022824 0.0001158 TRUE 0
## $r2_exp
## [1] 0
## 
## $r2_out
## [1] 0.25
## 
## $r2_exp_adj
## [1] 0
## 
## $r2_out_adj
## [1] 0.25
## 
## $correct_causal_direction
## [1] FALSE
## 
## $steiger_test
## [1] 0
## 
## $correct_causal_direction_adj
## [1] FALSE
## 
## $steiger_test_adj
## [1] 0
## 
## $vz
## [1] NaN
## 
## $vz0
## [1] 0
## 
## $vz1
## [1] NaN
## 
## $sensitivity_ratio
## [1] NaN
## 
## $sensitivity_plot

Working with MRraps

## $beta.hat
## [1] 0.00515672
## 
## $beta.se
## [1] 0.002410337
## 
## $beta.p.value
## [1] 0.03240175
## 
## $naive.se
## [1] 0.002368768
## 
## $chi.sq.test
## [1] 52.62634
##   over.dispersion loss.function    beta.hat     beta.se
## 1           FALSE            l2 0.005156720 0.002410337
## 2           FALSE         huber 0.006313638 0.002479360
## 3           FALSE         tukey 0.006002630 0.002477515
## 4            TRUE            l2 0.003985094 0.003767475
## 5            TRUE         huber 0.004148444 0.004721347
## 6            TRUE         tukey 0.004112417 0.004479062
## 
## MR-Lasso method 
## 
## Number of variants : 34 
## Number of valid instruments : 27 
## Tuning parameter : 0.3036984 
## ------------------------------------------------------------------
##  Exposure Estimate Std Error 95% CI       p-value
##  exposure    0.008     0.003 0.003, 0.013   0.003
## ------------------------------------------------------------------
## 
## Constrained maximum likelihood method (MRcML) 
## Number of Variants:  34 
## Results for:  cML-MA-BIC 
## ------------------------------------------------------------------
##      Method Estimate    SE Pvalue        95% CI
##  cML-MA-BIC    0.005 0.002  0.034 [0.000,0.010]
## ------------------------------------------------------------------
## 
## Debiased inverse-variance weighted method
## (Over.dispersion:TRUE)
## 
## Number of Variants : 34 
## ------------------------------------------------------------------
##  Method Estimate Std Error  95% CI       p-value Condition
##    dIVW    0.005     0.003 -0.001, 0.011   0.098   160.809
## ------------------------------------------------------------------
## 
## Mode-based method of Hartwig et al
## (weighted, delta standard errors [not assuming NOME], bandwidth factor = 1)
## 
## Number of Variants : 34 
## ------------------------------------------------------------------
##  Method Estimate Std Error  95% CI       p-value
##     MBE    0.010     0.006 -0.002, 0.021   0.102
## ------------------------------------------------------------------